Hydrofoil system



Jan. 5, 1965 R. LoPEz HYDRoFoIL SYSTEM 3 Sheets-Sheet l Filed Sep't.. 1.9, 1962 rNvENTor W SJNM BY W W AT'TORNEYS Jan. 5, 1965 R, LopEz HYDROFOIL SYSTEM 3 Sheets-Sheet .2

Filed Sept. 19, 1962 IN VEN TOR.

AT TORNEYS Jan. 5, 1965 R. LopEz HYDROFOIL SYSTEM 3 Sheets-Sheet 3 Filed sept. 19, 1982 INVENTOR. W W BY \-.LN\\

AT TORNEYS United States Patent Ofiice 3,164,117 HYDRV'JFOHl SYSTEM v Robert Lopez, Williamsport, Pa., assignor to Aqua-Elite Hydrofoil Corporation, New York, N .Y., a corporation of New York Filed Sept. 19, 1962, Ser. No. 224,814 12 Claims. (Cl. 114-665) This invention 'relates to hydrofoils.

. It is an object of the invention to provide an improved cantilever hydrofoil with different portions at different angles to the horizontal for obtaining more eficient operation and operation with forward swept leading edges. Another object is to combine an improved hydrofoil with a boat hull with a correlation that obtains stability of the hull when foil-borne and with the hydrofoil retractable into out-of-the-way positions.

Other objects of the invention relate to mechanism for retracting hydrofoils and for supporting them when in retracted position. One feature relates to automatic control of a rest stop to compensate for changes in the angle of attack of the hydrofoil. Other features relate to the connection of the hydrofoil to a boat hull and to tension elements for pulling the hydrofoil up from working position to retracted position, or at least to a position where the center of gravity moves over into a location to continue the movement of the hydrofoils into fully retracted position by gravity alone.

Other objects, features and advantages of the invention will appear or be pointed out as the description proceeds.

In the drawing, forming a part hereof, in which like reference characters indicate corresponding parts in all the views:

FIGURE 1 is a diagrammatic sectional view through a boat hull equipped with hydrofoils in accordance with this invention;

FIGURE 2 is an enlarged, sectional view taken on the line 2-2 of FIGURE 1 but with the hydrofoil facing in the opposite direction;

FIGURE 3 is an elevation of the lower portion of one of the hydrofoils of FIGURE 1, the view being on an enlarged scale as compared with FIGURE 1 and being taken at the line 3-3 of FIGURE 1;

FIGURE 4 is an elevation showing the connection of one of the hydrofoils to the boat hull and showing a portion of the apparatus for retracting the hydrofoil;V

FIGURE 5 is a top view, partly broken away andin section, of a portion of the mechanism of FIGURE 4, the mechanism being shown on an enlarged scale;

FIGURE 6 is an enlarged end view of the apparatus shown in FIGURE 4 when viewed from the right in FIGURE 4;

FIGURE 7 is Van end view, on a slightly reduced scale, of the hydrofoil and -rest stop shownin FIGURE .4, the view being taken on the left in FIGURE 4; and

FIGURE 8 is a top plan view of the structure shown in FIGURE 7.

FIGURE 1 shows a boat hull 10 having a deck 12 and having hydrofoils 14 and 14'. connected with opposite sides of thehull. The hydrofoil 14 has a strut portion 18 connected with the upper partof the rhull 10 by a pivot connection 20. The hydrofoil 14 has a dihedral portion 22 which preferably includes an upper dihedral portion 24 and a lower dihedral portion 26. In the preferred construction, there is a fin 28 extending downward and substantially normal to the lower dihedral portion 26. This fin is substantially lower than the foilborne water line of the hydrofoils.

The strut portion 18 extends downwardly and outwa-rdly away from the hull 10. The upper dihedral portion 24 3,164,117 Patented Jan. 5, 1965 merges with the strut portion 18 at a location where the hydrofoil changes its direction rather sharply. In the preferred construction, the upper dihedral portion 24 makes an angle of approximately 36 with the horizontal; and the lower dihedral portion 26 is at a somewhat lesser angle to the horizontal, the angle being preferably ap' proximately 20. These angles are given by way of illustration, but the maintenance of angles of this approximate value is advantageous in obtainng an eificient hydrofoil which turns easily when the boat is steered and which operates at high speed without drawing a bubble down into the water.

The foil-borne water line for the hydrofoils 14 and 14' is indicated by the reference Character 32. Most of the lower dihedral portion 26 is under water when the boat is lightly loaded. With heavy loads, all of the lower dihedral portion 26 is under Water and so is part of the upper dihedral portion 24. While the upper and lower portions of the dihedral of the hydrofoil 14 are at different angles to the horizontal, the hydrofoil can be made with both of these portions of the hydrofoil the same, though more efi'icient operation is obtained with the portion 26 at a lower angle than the portion 24.

In the preferred construction the strut portion 18 slopes downward and outward at a steep angle and the hull has rearward hydrofoils 33 and 33' generally similar to the forward hydrofoils 14 and 16 but with strut portions which slope downwardly and outwardly from the hull lt) at greater angle than that of the forward hydrofoils so that the water line of each rearward hydrofoil is further out than the water line of the corresponding forward hydrofoil, and especially when the boat is foil-borne. In practice it has been advantageous to have this increase equal to approximately 'one tenth of the fore-and-aft spacing of the hydrofoil water lines. This.

facilitates turning of the boat.

There is a platform 36 attached to the hydrofoil 14, preferably on the lower part of the strut portion 18. This platform 36 is below the water line when the hull 18 is fioating as a displacement hull and the platform 345 has some camber which makes it assist the other por.- tions of the hydrofoil in raising the hull in the water when initially starting the boat with ncreasing Velocity to make the hull foil-borne. Another important purpose of the platform 36 is to relieve the speed 4and shock of falling when for any reason the hydrofoils lose their lift and the hull comes down from its foil-borne posi tion and into contact with the water. Thus the platform 36 is located in a position where it will strike' the water either before or slightly after the hull 10 makes its initial contact with the water during downward movement of the hull from its foil-borne to its displacement condition.

The platform is closeenough to the top surface of the hydrofoil to cause turbulence in flow over the hydrofoil and displacement of weeds and grass that may accumulate on the foil. The platform is closer, therefore, than are the successive foils of ladder hydrofoils where it is desirable that each foil operate independently of the others.

is of the same construction as the which correspond to the hydrofoil 14 I The Vhydrofoil 14 can swing farther into its fully retracted position shownV in dotted lines and designated by the reference character 14B. The hydrofoil 14' is similarly movable into retracted positions indicated in dotted lines and designated by the reference. characters 14'A and-14B. The hydrofoil 14 is shownon an enlarged scale in PEG- URES,l Zdand 3. VThe hydrofoil has a leading edge 38 which slopes forwardly asit extends away from the cantileYer; ends at which theextension 28 is located. Thus the leading edge 3 8 extends progressively forward as it rises to the surface of the water. This has the advantage that weeds, or other fioating. debrisin the water, which engagesthe leadingedge 38 of'the hydrofoil, has a tendency to slide rearwardly along the leading edge 38 and to eventually come freeyof the hydrofoil at the free end of the extension 28. This makes the hydrofoils self-cleaning anddprevents the formation of bubbles whichwonld cause the hydrofoils to lose .their lift.

The hydrofoils 14 and 14' are moved from the working positions shown, in full lines in FIGURE 1 to the pantially retrated positions 14A and 14A by hoisting mechanisrn which is illustrated diagrarnrnatically in FIG- UR 1. This mechanismincludesa cylinder-and-piston hydraulie'motor 40 secured to a rigid portion 42 of the hoa't hull. The motor 40 has a piston 44.- to which two flexible cables 46 and 46' are connected. These cables 46 and passdaround pulley wheels 43 and 43' at the deck of the hull and then the iiexible cables pass outwardly toward the sides of the hull.

' The end of the flexible cab'le 45 which is remote from the pistonv rod 44 is connected by a pivot connection 49 to :a link andlthis link 50 is in turn Vconnected by .another pivot connection 52 to a bracket on the hydrofoil 14.

FIGUR 4 shows, on a larger Scale, the connection of the flexible cable 46 to the hydrofoil 14. The pivot connection 52 connects with abracket 56 whichis rigidly secured to the hydrofoilr14 and which extends beyond the hydrofoil 14 so that when the hydrofoil is in its working position, as shown in FIGURE 1, the link 50 can extend vertica'lly and the pivot connection 52 is at a lower level 'than the pivotV connection 20, that joins the hydrofoil to the boat 'hullfl The link 570 is long enough, however, 'to reach 'above the end of the hydrofoil 14 and to lorcatevthe vpivot connection 49 above the level of the pivot 20 V ,w

When 'the Vhydrofoil 14 is in working position, therefore, a horizontal pull by the flexible cable 46 on the pivot connection49' rocks the link 50 against the upper portion of the hydrofoil'14 and with this point of contactof'the link 50, With the upper part of 'the hydrofoil as' a fuicrum, the nnk 50 mqves dozkwise in FIGURE 1 and moves, the lower pivot connection 52, and the entire hydrofoil 14 to whichthis pivot connection 52 joins the link 50, in aclockwise direction about the `axis of the pivot 20. This movernent continues until the link 50 passes through a horizontal position and after the link reaches the horizontal position it exerts a direct pull on the pivot 52, as shown in FIGURE 4, without the necessity for any fulcrum about which the link 50 can rock. In FIGURB 4 the connection of the fiexible cable 46 to the link 50 is shown with a turnbuckle 56 for adjusting' the Veffective length of `the cable 46, particul'arly with respect to the corresponding cable on ythe other side of the 'no-at. f

. I'Tlsorder to-reduce the sizeof the motor 40 '(FIGURE 1),vthe power-retracting mechanism is designed so that it -moyes the hydrofoils into a partially retracted position in which the center of gravity of these hydrofoils is moved inward over the deck and inward ofV the pivot connections 20 ;and 20'. Further movement of the hydrofoils into fully. retracted position can then be accomplished by gnavity and this eliminates the necesrsity for having a motor 40 with a sufciently long stroke to move the hydrofoils to their fully retr'acted positions.

FIGURE 4 shows a rest stop 60 against which the hydrofoil 14 is supported when in fully retracted position. This rest stop 6G is in the form of a stirrup located at the upper end of a support 62.

FIGURE 5 is a top plan view of the structure shown in FIGURE 4. The hydrofoil 14' has portions on opposite sides of a bracket 54. The pivot connection 20 includes pins 56 which extend through these portions of the hydrofoil and into the brackets 64. There are set screws 68 for preventing the pins 66 from becoming displaced with respect to the bracket 64. There is a shear pin 70 extending through the bracket 64 and into a shaft '72. A retainer 74 holds the shear pin '70 in place, the retainer 74 being constructed of spring material and being connected rigidly to a side Wall of the bracket 4 by a fastening means such as screws 76.

The shaft '72 extends into a hollow shaft 78 and is secured to this hollow shaft '78 by a pin or bolt 80. This bolt 80 also attaches another bracket 32 to the hollow shaft 78.

Referring back to FIGURE 4, the hollow shaft 78 is supported by bearings 86 and 87, these bearings being attached to the deck 12 by a base plate 9h which has screws 92 extending 'through the deck and into a deck beam or other fixed part of the boat.

The hollow shaft 7% is free to turn in the bearings 8d and 87 except when held in an adjusted position by means which will be described. The portion of the bracket 82 below the hollow shaft 78 has a quadrant face 96; and the hydrofoil 14 has a boss 93 which bears against the quadrant face 96. A retainer 1% extends through` the hydrofoil 14, through the boss 98 and into the quadrant face 96. There is a threaded nut 10,2 which has threads into which the retainer wii screws to lock the hydrofoil 14 to the bracket 82. The retainer 190 has a handle portion 104 by which it is rotated to screw it into or unscrew it from the nut 102.

The retainer secures the hydrofoil 14 to the bracket 82 so as to hold the hydrofoil in working position. When the hydrofoil is to be retracted, the retainer 100 is removed and the hydrofoil 14 is swung upwardly about the pivot connection 20 into retracted position, as previously explained. When it is desired to change the angle of attack of the hydrofoils, the hollow shaft 78 is turned in the bearings 86 and 87 and this moves the bracket 82 angularly about the longitudinal aXis of the hollow shaft 78, and also moves the hydrofoils 14 about this same longitudinal axis since the shaft 72 which supports the hydrofoil bracket 64 has its axis coincident with the axis of the hollow shaft 78, as previously explained.

The support 62 for the rest stop 60 has a hub portion 106 which extends around the hollow shaft 73 and which is attached to the hollow shaft 78 by za screw 108. Thus the support 62 moves angularly whenever the hollow shaft 78 is turned and moves as a unit with the hollow shaft 78. Therefore, any adjustment of :the angle of attack of the hydrofoil 14 will result in a shift in the position of the rest stop 60 so as to compensate for the new position which the hydrofoil 14 will occupy when it is again moved into retracted position. This construction maintains the bottom of the rest stop, with which the hydrofoil 14 contacts, always parallel with the axis of the pivot connection 20. It is this axis of the pivot connection 20 which rocks about the axis of the hollow sh'aft 78 when the hollow shaft is moved to change the angle of attack of the hydrofoil.

The means for holding the hollow shaft 78 in any set position, for the desired adjustment of the angle of attack of the hydrofoils, is shown in FIGURES 4-6. There is a bracket 114 rigidly secured to the fixed bearing 87. The hollow shaft 78 extends beyond the inner end of the bearing 87 'and has a crank 116 connected to it by a bolt 118.

There is an indexing disk 120 connected to the bracket 114 by a bolt 122. This bolt extends through the bracket 114 land has a nut 124 on its other end. The nut 124 is adjusted, and locked in position, so as to leave the disk 120 free to rotate on the bolt 122 as an axle.

FIGURE 6 shows the face of 'the disk 120. This disk has a p'lunality of holes 126 located around the center of the disk but with each of the holes 126 at a different distance from the center of the disk; that is from the aXis of the bolt 122 about which the disk 120 is free to rotate.

There is a retainer 130 which extends through one of the holes 126 and into a hole in the end of the crank 116. This retainer 130 preferably has threads which screw into complement'ary threads in the hole in the crank 116. The retainer 130 has a handle portion 134 which makes it convenient to screw the retainer into and out of the crank without the use of tools.

For every different hole 126 in the disk 120 through which the retainer 130 is inserted, the crank 116 has to be in a slightly different angular position in order to bring the hole in the crank into alignment with the hole 126 through which the retainer 130 is inserted. In this way an accurate and finely graduated adjustment of the angular position of the crank 116, and the corresponding angle of attack of the hydrofoil, can be obtained.

The preferred embodiment of the inve'ntion has been illustrated and described, but changes and modifications can be made and some features can be used in different combinations without departing from the invention as defined in the claims.

What is claimed is:

1. The combination with a boat having a hull and power means for propelling the hull, of hydrofoils on opposite sides of the hull, the foil on each side of the hull including a strut connected with the hull, a dihedral portion of the foil extending as a cantilever from said strut and sloping inwardly and downwardly for a substantial portion of its length, both the leading and trailing edges of the dihedral portion of the foil where the foil enters the water at the foilborne Water line sloping rearwardly as they slope inwardly and downwardly and continuing the slope rearwardly and inwardly and downwardly to the free end of the cantilever structure, that part of the dihedral portion below the foilborne water line extending along a line that changes in direction so that an upper portion of the cantilever slopes at a greater angle than a lower portion whereby the angle of attack of said upper and lower portions change in different amounts as the result of yielding of the cantilever structure with change of load.

2. The combination described in claim 1 characterized by the slope of the upper portion of the dihedral portion of the foil being approximately 36 to a horizontal plane, and the slope of the lower portion being approximately 20 to a horizontal plane.

3, In a boat, having a hull With a deck extending inward from an upper end of the hull, hydrofoils at opposite sides of the hull, a pivot connection between each hydrofoil and the hull, the hydrofoil being movable on the pivot connection between a working position in which the lower end of the hydrofoil extends downward into the water and a retracted position in which the hydrofoil is located above the deck, an adjustable rest located above the deck in position to receive the hydrofoil when in retracted position, adjustrnent means for moving the pivot connection angularly in a plane through the axis of the pivot connection to change the angle of attack of the hydrofoil, and a connection between the adjustment means and the rest operable to move the rest into different adjustable positions that compensate the change in position of the pivot axis with changes in the angle of attack.

4. The construction described in claim 3 characterized by a tubular support for the pivot connection on which each hydrofoil swings between working and retracted positions, a hearing in which the tubular support turns about an axis extending athwartship to move the aXis of the pivot connection about the athwartship axis to change the angle of attack of the hydrofoil, a bracket connected with the rest and supported from the tubular support and movable angularly as a unit with tubular support as said tubular support turns about the athwartship axis.

5. In a boat having a hull, hydrofoils connected to opposite sides of the hull, deck means extending across the hull near the upper end thereof, brackets on top of the deck'means and connected thereto at opposite sides of the hull, bearings in the brackets extending athwartship, shaft means in the bearing of each bracket, the shaft means being rotatable in the bearing about an athwartship axis to change the angle of attack of the hydrofoil, a fitting on the end of the shaft means extending beyond the deck means at both sides of the hull and at the approximate level of the deck means, connecting means joining each of the hydrofoils to the hull including a pivot connection to the fitting, said pivot connection having a fore-and-aft axis and on which the hydrofoil swings from a working position to a retracted position overlying the deck means, and including a second connection comprising a bracket that extends down from the shaft means and that swings as a unit with the shaft means as said shaft means is rotated in the bearing to change the angle of attack, and a detachable fastening that holds the hydrofoil in fixed relation to the bracket at any angle of attack for preventing swinging of the hydrofoil about said fore-and-aft axis.

6. The combination with a boat hull of forward hydrofoils connected with the hull at a location intermediate the stern and stern of said hull andextending downwardly into the water at an angle to the surface of the water on both sides of the hull, rearward hydrofoils connected to the hull at a location farther aft than the forward hydrofoils and also extending downwardly into the water at an angle to the surface of the water, the hull having a width where it is connected with the rearward hydrofoils approximating the width of the hull where it is connected with the forward hydrofoils, the connections of the hydrofoils to the hull including a strut at the upper part of each hydrofoil, each strut being connected at its upper end With the hull, the struts of the rearward hydrofoils sloping out- Ward away from the hull as they extend downwardly and at an angle to the Vertical, which angle exceeds the angle of the forward struts to the Vertical, the excess slope of the length of the struts of the rearward hydrofoils being correlated to result in the rearward hydrofoils being spaced transversely from one another so as to enter the water at distances farther out from the fore-and-aft center line of the hull than do the forward hydrofoils to facilitate turning of the hull when foilborne.

7. The combination described in claim 6 characterized by all of the hydrofoils being connected with the hull by connections that are relatively fixed with respect to the Vertical axis whereby all of said hydrofoils maintain the same relative positions with respect to the hull during both straight and turning movements of the boat hull.

8. The combination described in claim 6 characterized by each of the hydrofoils having its upper strut portion connected with the hull at the upper part of said strut portion and extending downwardly and outwardly from the hull to a foil section that extends downwardly and inwardly, the foil section extending into the water and to a level below that of the bottom of the hull, the foil section below the foilborne water line of said foil section being a cantilever.

9. The combination described in claim 6 characterized by the foilborne water line of the rear hydrofoils on each side of the hull being at a distance from the fore-anrd-aft center line of the hydrofoil system which is greater than the corresponding spacing for the forward hydrofoils by a distance equal to approximately one-tenth of the foreand-aft spacing of the forward hydrofoils from the rear- `.vard hydrofoils at the foilhorne water linesV of the hydrofoils.

10. The combination with a boat hull,` of a hydrofoil having a strut portion, a pivot connectiontin the upper part of the stmt portion and the hull near the top of the hull, said pivot connection having a pivot axis extending in a generally fore-and-aft direction, the strut portion Vextending downwardly, when the foil is in working position, and then downwardly and inwardly with a dihedral portic-n at an angle to the strut, the dihedral portion being a cantilever extension from the strut, the location of the pivot being correlated With the Shape of the hydrofoii so Vthat the hydrofoil swings upwardly and inwardly until all -portions of the hydrofoil are inward of the connection of the strut With the hull, and characterized by the hydrofoil having a dihedral portion with parts that slope at different angles to a horizontal plan-e, an upper part of the dihedral portion sloping downwardly at a steeper angle to the horizontal plane than does a lower part of the dihedral portion, and a rearward'hydrofoil'connected to the boat hull and having a strut portion and a dihedral portion, the strut portion of the forward and rearward hydrofoils sloping downward and outward and with the outward slope ofV the rearward hydrofoil substantially greater than that of the forward hydrofoil.

11. In a boat hull having a deck, hydrofoils on opposite sides of the hull, a pivot connection between each hydrofoil and the hull and on which the hydrofoil swings about a fore-and-aft axis from a'downwardly-extending working position to a raised and retracted position, a bracket secured to the hull and extending below said pivot connection, detachable fastening means connecting the hydrofoil to the bracket to prevent movement of the hydrofoil about said pivot connection, a top element of the hydrofoil extendin above the pivot connection when the hydrofoil is in Working position, a flexible cable connected with the hydrofoil in position to pull athwartship on said top element to rock the hydrofoil about its pivot connection from working to retracted position, the pivot connection being at'the approximate level of the desk and correlated With the hydrofoil Contour .to provide clearance for the hydrofoil to swing in over the deck, power mechanisin operably connected'with the flexible cable for pulling in- Ward on the flexible Cable, the power rnechanisrn having an Operating range that moves' the hydrofoil from Working position to a raised position in which the center of gravity of the hydrofoil is over the deck and inboard of said pivot connection, the movernent of the hydrofoil inward from said raised position to a fully retracted position being by gravity and beyond the Operating range of said power mechanism as the Cable flexes and accuniulates slack.

12. In a boat hull having` a deck, hydrofoils on opposite sides of the hull, pivot connections between each hydrofoil and the hull and on which the hydrofoil swings from a downwardly-extending working position to a raised and retracted position, tension elements connected with the hydrofoils above the axes of the pivot connections and extending inwardly, mechanisrn operably connected with the tension elements for pulling inward on the tension elelments to raise the hydrofoils frorn working position into raised and retracted positions, the tension elements for each hydrofoil including a stiff link pivoally connected with an upper part of the hydrofoil below the upper end of the hydrofoil and extending above the upper end, and another tension element pivotally connected with the portion of the stiff link that extends above the upper end of the' hydrofoil, and including a pivot connection of the link to the hydrofoil with the aXis of the pivot connection extending generally parallel to the pivot connection of the hydrofoil to the hull and with said pivot connection of the link at a location outward from the pivot connection of the hydrofoils and the hull, and a surface on the hull side of the link at a mid-portion of the link and with which the link contacts as the upper end of the link is pulled inward to rock the hydrofoil about its pivot connection with the hull as the hydrotoil is swung angularly from its working position into a raised position, the pivot connection for the link to the hydrofoil being movable into a position above the pivot connection of the hydrofoil to the hull as the hydrofoil moves into rased position whereby further pull on the link swings its plvot connection With the hydrofoil inward and upward to Shift the h'drofoil into retracted position.

References Cited in the file of this patent UNITED STATES PATENTS 1,444-,491 Baldwin Feb. 6, 1923 2,274,20O Hill Feb. 24, 1942 2.887,979 Bader May 26, 1959 2,9l4,014 Carl Nov. 24, 1959 3,031,999 Bader May l, 1962 FOREIGN PATENTS 1,(}66,89'7 Germany Oct. 8, 1959 1,l79,702 France Dec. 22, 1958 OTHER REFERENCES The Rudder, August 1958, vol. 74, No. S (pages 6-8 and 58 relied on). 

1. THE COMBINATION WITH A BOAT HAVING A HULL AND POWER MEANS FOR PROPELLING THE HULL, OF HYDROFOILS ON OPPOSITE SIDES OF THE HULL, THE FOIL ON EACH SIDE OF THE HULL INCLUDING A STRUT CONNECTED WITH THE HULL, A DIHEDRAL PORTION OF THE FOIL EXTENDING AS A CANTILEVER FROM SAID STRUT AND SLOPING INWARDLY AND DOWNWARDLY FOR A SUBSTANTIAL PORTION OF ITS LENGTH, BOTH THE LEADING AND TRAILING EDGES OF THE DIHEDRAL PORTION OF THE FOIL WHERE THE FOIL ENTERS THE WATER AT THE FOILBORNE WATER LINE SLOPING REARWARDLY AS THEY SLOPE INWARDLY AND DOWNWARDLY AND CONTINUING THE SLOPE REARWARDLY AND INWARDLY AND DOWNWARDLY TO THE FREE END OF THE CANTILEVER STRUCTURE, THAT PART OF THE DIHEDRAL PORTION BELOW THE FOILBORNE WATER LINE EXTENDING ALONG A LINE THAT CHANGES IN DIRECTION SO THAT AN UPPER PORTION OF THE CANTILEVER SLOPES AT A GREATER ANGLE THAN A LOWER PORTION WHEREBY THE ANGLE OF ATTACK OF SAID UPPER AND LOWER PORTIONS CHANGE IN DIFFERENT AMOUNTS AS THE RESULT OF YIELDING OF THE CANTILEVER STRUCTURE WITH CHANGE OF LOAD. 